Degenerate Backlund transformation

  • V. A. Gor'kavyi
  • E. N. Nevmerzhitskaya Физ.-техн. ин-т низких температур НАН Украины, Харьков


A concept of degenerate B¨acklund transformation is introduced for two-dimensional surfaces in many-dimensional Euclidean spaces. It is shown that if a surface in $R^n, n \geq 4$, admits a degenerate B¨acklund transformation, then this surface is pseudospherical, i.e., its Gauss curvature is constant and negative. The complete classification of pseudospherical surfaces in $R^n, n \geq 4$ that admit degenerate Bianchi transformations is obtained. Moreover, we also obtain a complete classification of pseudospherical surfaces in $R^n, n \geq 4$, admitting degenerate Backlund transformations into straight lines.
How to Cite
Gor’kavyiV. A., and NevmerzhitskayaE. N. “Degenerate Backlund Transformation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, no. 1, Jan. 2016, pp. 38-51,
Research articles